A120623 Numbers n such that the n-th Catalan number C(2n, n)/(n + 1) is divisible by n/3 but not divisible by n.

3, 12, 18, 84, 99, 120, 198, 216, 273, 342, 432, 522, 540, 792, 828, 945, 975, 984, 990, 1035, 1071, 1323, 1377, 1512, 1548, 1575, 1710, 1755, 1863, 2052, 2106, 2226, 2385, 2442, 2790, 2928, 3009, 3015, 3132, 3198, 3483, 3672, 3807, 3915, 3996, 4212, 4428

Offset: 1

Author

Robert G. Wilson v, Jun 19 2006

Keywords

• nonn

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000108, A014847, A120622.

Programs

Mathematica

fQ[n_] := fQ[n_] := IntegerQ[ Binomial[2n, n]/(n(n + 1)/3)] && !IntegerQ[ Binomial[2n, n]/n]; Select[ Range@4463, fQ@# &]

Python

A120623_list, b = [], 1
for n in range(1, 10**5):
    if b % n and not (3*b) % n:
        A120623_list.append(n)
    b = b*(4*n+2)//(n+2) # Chai Wah Wu, Mar 30 2016

Extensions

Better description from Joel B. Lewis, Nov 15 2006